Fast Facts
- NUTS wins on smooth, single-peak problems: it was 2–4× faster, but struggled with curved ridges and failed to explore separated modes—while its diagnostics clearly flagged trouble.
- emcee handles easy problems, but beware hidden failures: on the multimodal test it gave confidently wrong mode weights, with little warning beyond a short-chain notice.
- dynesty was the safest for multiple modes and Bayes factors: it found all peaks and estimated evidence well, though its reported uncertainty was too optimistic.
- Choose for the problem, then verify: use NUTS for smooth models, dynesty for multimodality or evidence, and check convergence diagnostics—or test against an exact answer when possible.
Three Samplers, One Posterior: NUTS vs. emcee vs. Nested Sampling
Speed matters only after accuracy
A sampler can run quickly and still miss the answer. To compare NUTS, emcee and dynesty, I tested them against three problems with exact solutions: a simple posterior, a curved ridge and a multimodal frequency search.
On the smooth problems, all three recovered the right results. NUTS ran about two to four times faster in these tests. Its advantage came partly from JAX compiling the model and its gradients. The benchmark used small, low-dimensional problems, so those timings don’t predict every real-world run.
Hard shapes expose different strengths
The curved ridge slowed emcee most, though it still matched the reference. NUTS also needed more work, while dynesty handled the shape with little change. In this small test, none failed.
The multimodal problem changed the picture. NUTS chains stayed near their starting peaks, and its diagnostics clearly flagged trouble. Emcee found modes but assigned them the wrong probabilities; its usual output offered little warning. Dynesty found all three modes and estimated their weights well across repeated runs. However, its evidence error bars looked too small for this case.
Choose for the problem, then check
Use NUTS for smooth models when you can provide gradients. Use emcee when gradients aren’t available and the posterior likely has one mode, especially in low dimensions. Choose dynesty when you need Bayesian evidence or expect separated modes. It can cost more computation, and repeated runs can help test its uncertainty.
No sampler earns trust by reputation alone. Check diagnostics, compare repeated runs and, when possible, test the method on a problem with a known answer. That small step can reveal a fast result that is wrong.
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